Notes on the complex Sachdev-Ye-Kitaev model

TL;DR

This paper explores the complex Sachdev-Ye-Kitaev model, detailing its charge properties, effective action, density of states, and zero-temperature entropy, providing both analytical and numerical insights.

Contribution

It offers a comprehensive analysis of the charge dynamics and thermodynamics of the complex SYK model, including a novel relation between charge and Green function asymmetry.

Findings

Derived a universal relation between charge and Green function asymmetry.

Computed the charge compressibility using three numerical methods.

Presented a 2D bulk picture with free Dirac fermions for zero-temperature entropy.

Abstract

We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with $N\gg 1$ flavors and a global U(1) charge. We provide a general definition of the charge in the $(G,\Sigma)$ formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.